IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i20p2598-d657355.html
   My bibliography  Save this article

Nonstandard Hulls of C * -Algebras and Their Applications

Author

Listed:
  • Stefano Baratella

    (Dipartimento di Matematica, Università di Trento, Via Sommarive 14, I-38123 Povo, TN, Italy)

Abstract

For the sake of providing insight into the use of nonstandard techniques à la A. Robinson and into Luxemburg’s nonstandard hull construction, we first present nonstandard proofs of some known results about C * -algebras. Then we introduce extensions of the nonstandard hull construction to noncommutative probability spaces and noncommutative stochastic processes. In the framework of internal noncommutative probability spaces, we investigate properties like freeness and convergence in distribution and their preservation by the nonstandard hull construction. We obtain a nonstandard characterization of the freeness property. Eventually we provide a nonstandard characterization of the property of equivalence for a suitable class of noncommutative stochastic processes and we study the behaviour of the latter property with respect to the nonstandard hull construction.

Suggested Citation

  • Stefano Baratella, 2021. "Nonstandard Hulls of C * -Algebras and Their Applications," Mathematics, MDPI, vol. 9(20), pages 1-25, October.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2598-:d:657355
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/20/2598/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/20/2598/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2598-:d:657355. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.